Transcription of THREE DIMENSIONAL GEOMETRY - NCERT
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THREE DIMENSIONAL GEOMETRY - NCERT
THREE DIMENSIONAL GEOMETRY463 The moving power of mathematical invention is notreasoning but imagination. IntroductionIn Class XI, while studying Analytical GEOMETRY in twodimensions, and the introduction to THREE dimensionalgeometry, we confined to the Cartesian methods only. Inthe previous chapter of this book, we have studied somebasic concepts of vectors. We will now use vector algebrato THREE DIMENSIONAL GEOMETRY . The purpose of thisapproach to 3- DIMENSIONAL GEOMETRY is that it makes thestudy simple and elegant*.
THREE DIMENSIONAL GEOMETRY 465 Hence, from (1), the d.c.’s of the line are 2 22 2 22 2 22, , a b c l m n abc abc abc =± =± =± ++ ++ ++ where, depending on the desired sign of k, either a positive or a negative sign is to be taken for l, m and n. For any line, if a, b, c are direction ratios of a line, then ka, kb, kc; k ≠ 0 is also a set of direction ratios.
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